In our last post, we explored how the Microsoft Solver Foundation can be used to solve simple maximization/minimization problems from C#. The problem we looked at is the following: given a set of products, each with a unit cost, a reselling price, and a weight, how can we maximize profit if we have only a limited budget and a limited weight capacity available.

Expressing and resolving the problem for a particular set of inputs was rather easy. However, the example we presented was very static: the decisions, the goal and the constraints were completely hard-coded.

The real value I found in the Microsoft Solver Foundation is that it can be completely integrated in your .NET code, working with strongly-typed objects. Today, we will revisit the same example we presented previously, but our goal will be to make the optimization program “generic”, so that we can resolve the same prototypical problem, given any set of inputs.

At a high level, what we are looking for is a class which, given a collection of Products, a Budget and a Capacity, returns a “recommended” purchase quantity for each product, maximizing our profit:

While most of my posts tend to focus on software development, my background is in optimization. Unfortunately, I don’t get to use these two skillsets together too often, because most projects require fairly basic modeling, and because the tools they require do not always integrate well together.

Luckily, the project I am currently working on involved performing some optimization, from within a .NET application, which gave me an opportunity to investigate the Microsoft Solver Foundation, which comes with a free solver and provides a framework for leveraging existing commercial solvers.

What is a solver? In a nutshell, it is an algorithm designed to identify optimal input values to maximize a function, while satisfying constraints. Certain classes of problems can be solved very efficiently using known algorithms, while others require the use of heuristics – but in general, if you find yourself asking “what is the best combination of values for this situation”, chances are, a solver is the tool you should be using.

Rather than go into theory, let’s look at an illustration, which will hopefully give you a sense for what the Microsoft Solver Foundation can do for you, and how you can leverage it in your .NET applications.

The problem: cheap imports from Gadgetistan

Imagine the following situation. You are an enterprising individual, and realize that there is good money to be made by importing goods from the Republic of Gadgetistan, the neighboring country. You break the piggybank, invest in an old truck, drive over there and get ready to buy a truckload of the local specialties, Widgets, Sprockets and Gizmos.

The truck didn’t come cheap, so you have only 200 Rublars (the official currenty of Gadgetistan) left in your wallet – this is your Budget Constraint.

The truck user manual is very clear – the Capacity of your truck is 500 Kilograms. One pound more, and your wonderful truck could collapse in a sad heap of scrap metal. This is your Capacity Constraint.

A bit of market research yielded the following information about the main product: the buying Cost, the reselling Price, and the Weight for a unit of each of the main goods from Gadgetistan.

Cost (Rublars)

Price (Rublars)

Weight (Kgs)

Widget

10

30

50

Sprocket

15

30

20

Gizmo

25

60

80

Your problem at that point is simple: how many units of each product should you carry in your truck, to make the most of your trip?